Characterization of a novel Optical Micro-machined Ultrasound Transducer

(1)

Delft University of Technology

Characterization of a novel Optical Micro-machined Ultrasound Transducer

Leinders, Suzanne DOI 10.4233/uuid:474e53d4-de7a-483a-9ce8-18eb99f902fa Publication date 2017 Document Version Final published version

Citation (APA)

Leinders, S. (2017). Characterization of a novel Optical Micro-machined Ultrasound Transducer. https://doi.org/10.4233/uuid:474e53d4-de7a-483a-9ce8-18eb99f902fa

Important note

To cite this publication, please use the final published version (if applicable). Please check the document version above.

Copyright

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy

Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim.

This work is downloaded from Delft University of Technology.

(2)

Characterization of a novel

Optical Micro-machined Ultrasound Transducer

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magniﬁcus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 11 december 2017 om 12:30 uur

door

Suzanne Margriet LEINDERS

(3)

Dit proefschrift is goedgekeurd door:

promotor: prof. dr. ir. N. de Jong promotor: prof. dr. H.P. Urbach co-promotor: dr. ir. M.D. Verweij

Samenstelling promotiecommissie:

Rector Magniﬁcus, voorzitter

prof. dr. H.P. Urbach, Technische Universiteit Delft, promotor prof. dr. ir. N. de Jong, Technische Universiteit Delft, promotor dr. ir. M.D. Verweij, Technische Universiteit Delft, co-promotor

onafhankelijke leden:

prof. dr. ir. A. van Keulen, Technische Universiteit Delft prof. dr. ir. R. Baets, Ghent University

prof. dr. A.G.J.M. van Leeuwen, Universiteit van Amsterdam prof. dr. S. Manohar, Universiteit Twente

prof. dr. ir. A.F.W. van der Steen, Technische Universiteit Delft / Erasmus MC, reservelid

This research was supported by the IOP Photonic Devices programme of NL-Agency of the Dutch Ministry of Economic Aﬀairs (project number IPD100026) and by TNO.

This free electronic version of this thesis can be downloaded from: http://repository.tudelft.nl

ISBN 978-94-028-0870-4

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the author.

(4)

Summary

We design and demonstrate a prototype ultrasound sensor based on a photonic micro-ring resonator integrated on a silicon membrane, and show that it can de-tect very low pressure ultrasound waves. The use of integrated photonics in future array transducers has several beneﬁts: for instance it provides a small spatial footprint, compatibility with MRI due to the lack of electrical wiring, easy interro-gation of the array of elements and ease of mass production, which may result in cost-eﬀective fabrication of array transducers. To understand the working princi-ple of the sensor, we have modeled the basic sensor element, fabricated the sensor and measured the response of the sensor to ultrasound. We have studied the re-sponse of the optical resonator separately before we integrate the resonator on the membrane and measure the response of the entire sensor. Besides the characteri-zation of the sensor, we have expanded the existing knowledge of acoustical noise to determine the noise mechanism of the sensor.

Although ultrasound sensors are widely used in both industrial and medical ap-plications, this thesis mainly focuses on use in medical diagnostics. Currently, ultrasound transducers are amongst others used to image such diverse objects as the coronary arteries, heart valves, liver, kidneys, prostate, brain and thyroid, but the most familiar application is the echo imaging of the fetus. The basis of the conventional ultrasound transducer consists of piezoelectric material that converts an electrical signal into a pressure wave and vice versa. During the last decades the single element transducers are replaced by one-dimensional arrays of sensors and during the last few years we have seen the emergence of two-dimensional ar-rays of sensors. Hence the development is focused on miniaturization of the sensor elements and fabrication of large dense arrays.

In this thesis, we have designed the basic element of a possibly future array ultra-sound sensor that is based on integrated photonics. We have used the resulting

(5)

iv

Optical Micro-machined Ultrasound Sensor (OMUS) to investigate the working principle. The element consists of a silicon optical waveguide that is coupled to a photonic racetrack-shaped optical resonator with a spatial footprint of 50 µm by 10 µm. The optical resonator is positioned on a silicon-dioxide membrane with a thickness of 2.5 µm and a diameter of about 100 µm. When a pressure wave is incident on the element, the membrane deforms and thus deforms the optical resonator. The deformation of the optical resonator shifts the optical resonance frequencies. This shift is recorded by an external interrogation system.

We have fabricated the photonic circuit of the sensor in a semi-industrial CMOS line. The resulting wafer-piece (die) contains 220 nm high and 400 nm wide silicon waveguides on top of a 2 µm thick silicon-dioxide layer on top of a 250 µm thick silicon substrate. Next, we have deposited a 0.5 µm thick silicon dioxide cladding on top of the die to isolate the waveguide from the water. Finally, we have created the membrane by locally removing the entire silicon substrate with use of deep reactive ion etching from the back of the die.

The prototype sensor is used to give proof of concept. We have used a laser and photo-receiver to interrogate the optical resonator and a conventional ultrasound transducer to transmit the pressure waves that were received by the sensor. We have found that the sensor had a resonance frequency of 0.76 MHz with a -6 dB bandwidth of 19 %. Furthermore, we have demonstrated that this prototype is ca-pable of detecting pressures as low as 0.4 Pa. The latter matches the performance of the state of the art piezo-electric transducers while the spatial footprint of our sensor is 65 times smaller.

The sensor elements were further investigated by characterizing the strain-induced shift of the resonances of the optical resonator. We have applied a well defined strain to the racetrack resonators and have identified three different influences on the shift of resonances; dispersion, change in effective index and change in track-length. We have found that the linear wavelength shift per applied strain varies between 0.5 and 0.75 pm/microstrain depending on the width of the waveguide and the orientation of the silicon crystal for infrared light around 1550 nm wave-length. The influence of the increasing ring circumference is about three times larger than the influence of the change in waveguide effective index, and the two effects oppose each other.

The inﬂuence of the membrane is investigated by applying increasing static load-ings to the sensor. In this study, we have integrated a short optical resonator on the membrane, which experiences a radial deformation rather than a uniform elongation. The measurement results show a non-linear response with high sen-sitivity at the beginning of the curve where small loadings are applied and lower sensitivity to the larger loadings.

The dynamic behavior of the sensor is investigated with a laser vibrometer. Due to simultaneous read-out of the sensor and the vibrometer, the read-out of the sensor can be compared to the vibration of the membrane and vibration of the entire sensor. We were able to show that the sensitivity of the sensor to low pressure signals is indeed induced by the membrane of the sensor, as the back of the sensor shows no signiﬁcant vibrations. Furthermore, we have shown that the resonance frequency of the sensor can be tuned using diﬀerent membrane diameters.

(6)

v

The noise level of our sensor is different from conventional ultrasound transducers due to the lack of electrical circuits. The noise of the optical sensor is only caused by acoustical noise, which is not well described in literature. Therefore, we have expanded the existing knowledge of acoustical noise by analyzing two mechanisms of acoustical noise. We show that in thermodynamic equilibrium the noise power delivered by the medium to the sensor balances the noise power delivered by the sensor to the medium. Moreover, we show that for sensors with vanishing aperture area, the noise pressure due to the molecular motion in the medium will reach a well-defined finite limit.

(7)

(8)

Samenvatting

In dit proefschrift ontwerpen en demonstreren we een prototype ultrageluidsen-sor die bestaat uit een optische micro-ring-resonator op een silicium membraan. We laten zien dat deze sensor zeer lage ultrageluid drukgolven kan detecteren. Het gebruik van ge¨ıntegreerde optica in toekomstige matrix tranducenten heeft verschillende voordelen: de technologie past bijvoorbeeld op een klein oppervlak, is te combineren met MRI omdat er geen elektrische bedrading nodig is, maakt dat een matrix van elementen makkelijk uitleesbaar is en is via massa productie te produceren hetgeen mogelijk resulteert in kosteneﬀectieve fabricatie van matrix transducenten. Om de werking van de sensor te begrijpen hebben we een model ge-maakt van het basis element, deze sensor gefabriceerd en de respons op ultrageluid gemeten. We hebben eerst apart de respons van de optische resonator bestudeerd voordat we de resonator in het membraan hebben ge¨ıntegreerd en de respons van de hele sensor hebben gemeten. Naast het karakteriseren van de sensor hebben we de bestaande kennis van akoestische ruis verruimd om het ruismechanisme van de sensor te kunnen bepalen.

Hoewel ultrageluidsensoren worden gebruikt in zowel industriële als medische toe-passingen, focust dit proefschrift zich op de medische diagnostiek. De meest be-kende toepassing hierin is de echo van een foetus, maar de ultrageluidsensoren worden ook gebruikt om beelden te maken van allerlei objecten zoals de krans-slagaders, hartkleppen, lever, nieren, prostaat, hersenen en schildklier. De basis van de conventionele ultrageluidtransducenten bestaat uit piëzo-elektrisch materi-aal dat een elektrisch signmateri-aal in een drukgolf converteert en andersom. Al sinds tientallen jaren hebben enkel-elementstranducenten plaatsgemaakt voor een é´ en-dimensionale array van transducentelementen. Als gevolg daarvan heeft de ont-wikkeling zich met name gericht op het verkleinen van de transducentelementen en het fabriceren van matrices met hoge dichtheid van elementen.

(9)

viii

In dit proefschrift hebben we het basis element ontworpen van een mogelijk toe-komstige matrix ultrageluidsensor dat gebaseerd is op ge¨ıntegreerde optica. We hebben de resulterende optische micro-gefabriceerde ultrageluidsensor (OMUS) gebruikt om de werking daarvan te onderzoeken. Het element bestaat uit een optische golfgeleider van silicium die aan een optische ellips-vormige resonator wordt gekoppeld. Deze resonator heeft een spatieel oppervlak van 50 µm bij 10 µm. De optische resonator is gepositioneerd op een membraan van silicium-dioxide dat een dikte heeft van 2.5 µm en een diameter rond de 100 µm. Wanneer een drukgolf het element raakt vervormt het membraan en daarmee ook de optische resonator. De deformatie van de optische resonator zorgt voor een verschuiving van zijn optische resonantiefrequenties. Deze verschuiving wordt geregistreerd door een extern uitlees systeem.

We hebben het optische circuit van de sensor in een semi-industri¨ele CMOS lijn gefabriceerd. De resulterende silicium schijf (wafer) bevat 220 nm hoge en 400 nm brede silicium golfgeleiders op een 2 µm dikke siliciumdioxide laag op een 250 µm dik slicium substraat. Hierna hebben we de golfgeleiders met een 0.5 µm dikke laag slicium bedekt om de golfgeleiders van het water te isoleren. Tenslotte hebben we het membraan gemaakt door lokaal via de achterkant met een diepe reactieve ion ets het volledige silicium substraat te verwijderen.

Het prototype sensor is gebruikt om te laten zien dat het concept werkt. We hebben gebruik gemaakt van een laser en fotodiode om de optische resonator uit te lezen en een conventionele ultrageluidtranducent om de drukgolf op te wekken. We hebben een resonantie frequentie van 0.76 MHz gevonden met een -6 dB band-breedte van 19 %. Verder laten we zien dat dit prototype een minimale druk van 0.4 Pa kan detecteren. Deze druk komt overeen met die van de meest moderne pi¨ezo-elektrische trandsucenten terwijl het oppervlak van onze sensor 65 keer klei-ner is.

De sensorelementen zijn verder onderzocht door het karakteriseren van de rek-ge¨ınduceerde verschuiving van de resonanties van de optische resonatoren. We hebben een goed gedefinieerde rek aangebracht op de ellips-vormige resonatoren en hebben drie verschillende invloeden op de resonatieverschuiving kunnen on-derscheiden; dispersie, verschil in effectieve index en verschil in baanlengte. We hebben voor infrarood licht met een golflengte rond 1550 nm een variatie tussen 0.5 en 0.75 pm/microrek van de lineaire golflengte-verschuiving per aangebrachte rek gevonden, die afhankelijk is van de breedte van de golfgeleider en de oriëntatie van het silicium kristal. De invloed van de toenemende baanomtrek is ongeveer drie keer zo groot als de invloed van het verschil in de effectieve index van de golfgeleider. Daarnaast werken de twee effecten tegengesteld.

De invloed van het membraan is onderzocht door een toenemende statische last op de sensor aan te brengen. In dit onderzoek is een korte optische resonator op het membraan ge¨ıntegreerd, die een radi¨ele deformatie ondervindt in plaats van een uniforme verlenging. De meetresultaten laten een niet-lineaire respons zien met hoge gevoeligheid in het begin van de curve waar kleine lasten worden aangebracht en lagere gevoeligheid voor de hogere lasten.

Het dynamische gedrag van de sensor is met een laservibrometer onderzocht. Door het gelijktijdig uitlezen van de sensor en de vibrometer kan de meetwaarde van de

(10)

ix

sensor vergeleken worden met de vibratie van het membraan en de vibratie van de gehele sensor. Hierdoor kunnen we laten zien dat de gevoeligheid van de sensor voor lage druk signalen inderdaad door het membraan wordt ge¨ınduceerd omdat de achterkant van de sensor geen signiﬁcante trillingen laat zien. Verder laten we zien dat de resonantiefrequentie van de sensor kan worden be¨ınvloed door gebruik van membranen met verschillende diameter.

Het ruisniveau van onze sensor verschilt van conventionele ultrageluidsensoren door het ontbreken van elektrische circuits. De ruis van de optische sensor wordt alleen veroorzaakt door akoestische ruis, die niet goed is beschreven in de lite-ratuur. Daarom hebben we de bestaande kennis van akoestische ruis uitgebreid door twee ruismechanismen van akoestische ruis te analyseren. We laten zien dat in thermodynamisch evenwicht het ruis vermogen dat door de omgeving aan de sensor wordt afgegeven in balans is met het ruis vermogen dat door de sensor aan zijn omgeving wordt afgegeven. Bovendien laten we zien dat voor sensoren met een oneindige klein oppervlak de ruis druk door moleculaire beweging in het medium een goed gedeﬁnieerde eindige limiet bereikt.

(11)

(12)

1

General introduction

This thesis describes the development and characterization of an ultrasound sen-sor based on integrated photonics. The use of light as information carrier makes this sensor diﬀerent from the state-of-the-art piezo-electric ultrasound transducers. It provides a large data transfer capacity due to a broad bandwidth. Moreover the sensor is made using standard Complementary Metal Oxide Semiconductor (CMOS) fabrication processes, which allows for mass production. To design a high quality sensor that has comparable or even better image qualities than the state-of-the-art transducers, complete understanding of the sensor is necessary. Therefore we investigated the optical, mechanical and acoustical aspects of the sensor.

This chapter starts with an introduction of the main background of medical imag-ing and development of conventional ultrasound transducers (Sec. 1.1). Then we describe the aim of the research that was carried out in Sec. 1.2. In this part, we brieﬂy describe the working principle of the sensor to get some understanding of the sensor. For a detailed description of the sensor as well as its operating principle we refer the reader to Chapter 4. In Sec. 1.3 we will discuss the development in the use of guided light in sensors and the semiconductor industry as fabrication platform. The outline of this thesis is presented in Sec. 1.4.

1.1 Medical imaging

Medical ultrasound is often used for diagnostic imaging of patients. Compared to other imaging techniques as CT and MRI, it has a lot of beneﬁts; the images are real-time, it is safe (no radiation), inexpensive and the system is portable. The name ultrasound imaging refers to the use of high (≥ 1 MHz) frequency sound waves to image the inside of the body. A device, named transducer, is used to

(17)

2 Chapter 1. General introduction

emit soundwaves into the body. These waves partly reflect on the inhomogeneities inside the body. The transducer receives the reflected waves (echoes) and with use of the time of flight the axial depth of the tissue can be determined. A single trans-mission provides the location of the scatterers in the beam line of the transducer. To create an image, multiple lines are needed and hence the area of interest has to be scanned. Three typical ultrasound images are shown in Figure 1.1 with on the left an image of a fetus, in the middle an image of the 4 chambers and valves of the heart and on the right an ultrasound image of an artery.

The development of diagnostic ultrasound instrumentation as we know it today was initiated around the time of the end of the Second Wold War [1]. The conventional transducers used to make an image consist of piezoelectric material. Piezoelectric-ity is defined as an electrical polarization related to mechanical strain. The polar-ization is proportional to the strain and changes sign with it [2]. Thus piezoelectric materials accumulate an electric charge in response to an applied mechanical stress and vice versa. The first ultrasound transducers were made of Quartz. This ma-terial has a high mechanical strength and low internal friction, but needs large amplitude voltages to be driven. Later, piezoelectric ceramics were used which had an improved efficiency and could be processed into varying shapes and sizes. In 1954, lead titanate-zirconate compositions (PZT) were discovered as piezoelec-tric material which had the additional benefits of a larger operating temperature range [3]. Currently, PZT is still used as transduction material in the state-of-the-art transducers, while research for new materials like single crystals (e.g. Lead Magnesium Niobate-Lead Titanate (PMN-PT)) or composites continues [1]. The efficiency of a transducer in conversion of energy depends next to the material on the frequency of excitation. To improve the energy transfer between the piezo-electric material and the tissue, matching layers and backing layers are often used. A scheme of a conventional transducer is shown in Figure 1.2. This transducer contains a large backing block that prevents movement of the bottom part of the piezoelectric layer. The matching layer, which has an impedance in between the piezoelectric material and the tissue, is here indicated as plastic ’nose’.

Next to the development of new materials, other aspects of the transducers were also adapted. The transducers changed from single element transducers into ar-rays, which contain many small transducer elements in a line (linear array) or in a plane (matrix array). Arrays give the option to illuminate an entire area at once, or electrically scan the area of interest [1]. With these arrays higher resolution images could be obtained with a much faster acquisition time [4].

The transducers used for medical imaging are designed for specific applications. The materials, element dimensions, shape and resonance frequency are optimized to obtain the penetration depth and resolution needed for each procedure. The ap-plications that require dense arrays with small outer dimensions of the transducer are the ones where our sensor can provide most added value. Such applications can be found in the field of intra-operative image guidance (e.g. Intravascular Cardiac Echography (ICE)), where the device should not interfere with the proce-dure [5], or in the field of internal medical diagnostics, for instance Transesophageal Echocardiography (TEE) or Intravascular Ultrasound (IVUS). In these last two diagnostic applications the transducer is positioned on a catheter which is

(18)

posi-1.1. Medical imaging 3

tioned inside the body. With a TEE image the catheter containing the transducer is positioned via the mouth or nose in the esophagus to image the hart. In case of IVUS the catheter is positioned inside a coronary artery to image the artery wall. In both cases a small transducer is required that nevertheless consists of multiple elements. Because the transducer is mounted on a catheter, the number of coaxial cables that connects the catheter to the computer is also limited, which provides an additional design challenge.

1 mm

a) b) c)

Figure 1.1: Ultrasound images of a) fetus obtained with 3D ultrasound [6],

b) apical 4-chamber view of the heart obtained with transthoracic echocardio-graphy [7] and c) a cross-section of a coronary artery obtained with IVUS [8].

(19)

1.2 An optical micro-machined ultrasound sensor

for (medical) ultrasound

The aim of this research project was to design, fabricate and test an ultrasound sensor based on a new operation principle. This operation principle makes use of integrated photonics. Therefore our read-out system tracks the light spectrum over time. When an acoustical wave is incident on the sensor the transmission spectrum changes. We can explain this by describing the working principle of the sensor. The sensor consist of a photonic waveguide (bus waveguide) that guides the light from one side of the sensor towards the other side. We positioned a pho-tonic ring resonator, which is a looped waveguide with distinct resonances, in the middle of the sensor. A part of the light spectrum is coupled from the photonic waveguide into this ring resonator. When we transmit a broad light spectrum through the bus waveguide and record the transmission spectrum at the end of the waveguide, instead of a ﬂat spectrum we measure resonance dips consistent with the resonance frequencies of the ring resonator. We want to obtain a modu-lation of this spectrum due to ultrasound waves. This is done by positioning the ring resonator on an acoustical membrane. When a pressure wave is incident on the acoustical membrane, the membrane and thus the integrated ring resonator will deform. The deformation of the ring resonator inﬂuences the position of the resonances in the transmission spectrum. When one resonance is monitored over time using light with a very narrow spectrum, an incident pressure wave causes a time dependent shift of this resonance dip, which is observed as a modulation of the transmitted light intensity.

A main beneﬁt of this new operating principle is the sensors in-susceptibility to electromagnetic interference. Therefore the sensor can be used in combination with MRI and other radiative environments. An other advantage is the possibility to stack data of several sensors in the spectrum. As a result only a single ﬁber is required as read-out of an entire array.

To get a good understanding of this sensor and be able to determine the feasibility as ultrasound sensor we investigated several aspects. We studied the optical com-ponents on the chip [10] as well as the influence of strain on the ring resonators (Chapter 3). We provided proof of concept with the first ultrasound measure-ments performed with a prototype (Chapter 4). We determined the influence of the membrane with a static pressure analysis and a study of the membrane motion (Chapter 5). Finally we derived a theory about the noise pressure levels that de-termines the minimal pressure level that can be measured with this type of sensor (Chapter 6).

1.3 Integrated

photonic

systems

and

micro-machining fabrication technology

Our sensor uses light as information carrier to benefit from fiber optics. Fiber op-tics, first developed in the 1970s, revolutionized the telecommunications industry. Compared to copper wires, optical fibers have the benefit of low attenuation and

(20)

1.4. Outline of this thesis 5

interference, high reliability over long distances, a long life span and a very high information capacity [11].

We choose silicon and silicondioxide as materials for the index-guided based pho-tonic waveguides. This allows us to use silicon-on-insulator technology for fabrica-tion and hence proﬁt from 50 years of development in semiconductor fabricafabrica-tion technology. This mainly means ease of fabrication and hence mass production. Chip production today is based on photolithography. In this process high energy UV-light is shone through a mask upon a photosensitive ﬁlm covering the silicon wafer. The illuminated part of the photosensitive layer forms the pattern of the chip and is developed into a layer that protects the underlying silicon. With etch-ing processes the silicon that is not protected by the mask is removed. The wafer is cleaned by removing the mask. Most designs require several of these fabrication sequences [12].

Lots of structures can be created with this fabrication technique, but there are lim-itations that have to be taken into account when a design is made. For instance, there are variations present in the height of the silicon light-guiding layer and the chip can contain structures that have a slightly different size than designed for. Furthermore the lithography can only be optimized for one feature size, meaning that only this feature size is according to specifications. A final consideration is the fact that the sides of the patterns are not perfectly straight, but have an angle of about 10 degrees [10].

1.4 Outline of this thesis

With this brief introduction to the different fields involved we have obtained a general idea why this new sensor can be of importance to the medical field. In the remaining part of this thesis, we discuss the work done to obtain this sensor as well as the investigation of the different aspects of the sensor.

Chapter 2 presents a short overview of the theory that is important for the design of our sensor. It ﬁrst describes the basic concepts that we used to model the sensor. The second part of this chapter describes the modeling results. With the models we obtained possible dimensions and corresponding resonance frequencies for our prototype device. We also calculated the ﬁrst values of the pressure levels that could be received.

Chapter 3 studies the shift in the optical resonances due to an applied static me-chanical strain to the ring resonator. The influence of different physical aspects on the ring resonator is investigated, such as: the elongation of the track, the change in cross-section of the waveguide due to the Poisson ratio, the change in the refractive index of the silicon and silicondioxide due to the photo-elastic effect and the dispersion in the waveguide.

Chapter 4 presents the proof-of-concept of the sensor. We present the ﬁrst mea-surement results of the response of our sensor to an acoustical pressure wave. We determined the transfer function and hence its resonance frequency. We found a noise equivalent pressure that indicated that we fabricated a very sensitive ultra-sound sensor.

(21)

Chapter 5 describes the characterization of the sensor. We investigated what the behavior of the sensor is under static and dynamic loading as well as the initial shape. Due to the fabrication technique of the silicon wafer, we found that initial strain is present, which influences the behavior of the membrane. Instead of linear theory, large deflection theory is needed to understand the static pressure mea-surements. Furthermore it is shown that only the membrane itself is significantly responding to the ultrasound waves.

Chapter 6 presents a theory to determine the noise level of small sensors. The noise ﬂoor of our sensor is diﬀerent from the state-of-the-art transducers due to the lack of piezoelectric material. Hence our sensor is only prone to the noise generated by thermal motion of the atoms in the membrane and the water, while the piezoelectric transducers also have to deal with the high electrical noise from the electrical impedance.

(22)

Chapter

2

Basic concepts and

membrane design

Abstract – To be able to design a prototype sensor the basic concepts of the sensor

should be known. This chapter describes the basis concepts of photonic waveguides, couplers and ring resonators as well as the linear theory for membrane deﬂection. With use of these concepts the membrane thickness and diameters are obtained. It is shown that a membrane thickness of 1.2 µm of silicon left underneath the 2.5 µm silicondioxide results in the most induced strain in the layer of the photonic waveguide for a resonance frequency of 1 MHz. Membrane diameters from 60 to 100 µm result in resonance frequencies of 3.2 to 0.9 MHz in water. Calculations showed a minimum detectable pressure level in the order of 600 Pa, which is suﬃcient for ultrasound sensing.

This chapter is based on the following publication:

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M. J. van Neer, K. W. A. van Dongen, H. P. Urbach, N. de Jong, and M. D. Verweij, “Membrane design of an all-optical ultrasound receiver,” in Proceedings IEEE International Ultrasonics Symposium, Prague, Jul. 2013, pp. 2175–2178

(23)

8 Chapter 2. Basic concepts and membrane design

The general concept of the sensor is that the transmitted light traveling through the optical waveguide is modulated by the mechanical deformation of the optical ring resonator due to an incident ultrasound wave. To design such a sensor we need to understand the concepts of guided light and its mechanical response to pressure. An overview of the main concepts is given in the first part of this chapter, starting with the theory of photonic waveguides followed by the linear theory of membrane deflection. The second part shows the first modeling results for the dimensions and the corresponding resonance frequency of the sensor. These are used to obtain an estimate for the membrane diameter and thickness as starting values for the design of the prototype.

2.1 Photonic waveguides

This section describes the theory for high-index-contrast silicon waveguides. It only describes the theory that is of interest in our design. The reader is referred to [10] for a broader description of the theory and newly derived theory for these kind of waveguides. We start with the description of waves that can propagate in a waveguide (Section 2.1.1). Then the coupling of light from the straight waveguide towards the ring resonator via a directional coupler is described (Section 2.1.2) and we ﬁnalize with the description of a ring resonator (Section 2.1.3).

2.1.1 General description of a dielectric photonic waveguide

Photonic waveguides conﬁne light and transport it over a given distance. The conﬁnement is done by index guiding where the core of the waveguide has a higher refractive index than the surrounding. The photonic waveguides that are discussed are rectangular waveguides made of silicon. They have a SiO2 burried

oxide (BOX) substrate and an air or SiO2cladding. The waveguides have a typical

height of 220 nm and width of 400 nm. The assumed free-space wavelength λ of the light is 1.55 µm. A schemamtic picture of such a silicon-on-insulator (SOI) waveguide is shown in Figure 2.1a, with its fundamental transverse electric (TE) mode depicted in Figure 2.1b. The fundamental mode has most of its energy in the

n1 = 3.45 n5 = 1 n4 = 1.44 n2 = 1 n3 = 1 (b) SiO₂ n = 1.44 air n= 1 Si n = 3.45 450nm 220nm y x (a)

Figure 2.1: Cross-section of a SOI waveguide. a) Sketch of the waveguide

b) Sketch of the Ex component of the fundamental mode in color. Dark blue

(24)

2.1. Photonic waveguides 9

center of the waveguide. The modes can be described with Maxwell’s equations. In our description we approximate silicon and silicon dioxide as linear dielectrics with permittivity ϵ, which means that the material polarization is proportional to the electric ﬁeld. We neglect magnetic behavior of the dielectrics by using the permeability of vacuum µ0. All optical descriptions given are valid for

monochro-matic light with angular frequency ω and vacuum wavelength λ = ω/2πc where c is the speed of light in vacuum. The physical electromagnetic fields are described by the real components of the complex vector fieldsE and H of the electric and magnetic fields respectively. Maxwell’s complex equations for monochromatic light in an isotropic linear dielectric medium without charges are given by [13]

∇ × E = −iωµ0H, (2.1)

∇ × H = iωϵE, (2.2)

∇ · ϵE = 0, (2.3)

∇ · H = 0. (2.4)

The latter two equations (2.3) and (2.4) are not independent and follow di-rectly from the ﬁrst two equations (2.1) and (2.2). The refractive index n depends on the permittivity as n = √ϵ/ϵ0, with ϵ0 the permittivity of vacuum. The

permittivity proﬁle ϵ(x, y, z) describes the devices as is indicated in Figure 2.1a and hence describes how the electromagnetic ﬁeld behaves.

Electromagnetic ﬁelds in a homogeneous isotropic medium without charges obey the wave equations

(∇2+ n2k2)E = 0, (2.5)

(∇2+ n2k2)H = 0, (2.6)

with k = ω/c the free-space propagation constant [13, Ch. 9]. A dielectric waveg-uide is fully described by its permittivity proﬁle ϵ(x, y) which is invariant in the z-direction, i.e. the direction in which the light propagates. We may assume that the propagating wave solutions have the form

E(x, y, z) = E(x, y)e−iβz_, _{H(x, y, z) = H(x, y)e}−iβz_, _(2.7)

with β the propagation constant.

To ﬁnd a solution in the form of Eq. 2.7 for the light propagation through rect-angular dielectric waveguides, we can use the extended description of Marcatili’s approximate analytical approach [14] or numerical mode solvers.

The field on the chip has to deal with losses. These losses are introduced by im-perfections of the silicon and by waveguide bends. In case of the waveguide bends the mode in the bend changes with respect to the mode of the straight waveguide. This happens because the wave fronts at the outside of the bend have to propagate faster than the wave fronts at the inside. As a result the power of the mode moves towards the outside of the bend [15]. This effect is stronger for sharper bends. When we include losses the electrical field of the TE mode is described by

(25)

with αp the propagation loss.

The eﬀective index is often expressed in terms of the propagation constant as ne≡

β

k. (2.9)

The eﬀective group index ng is deﬁned as

ng≡

∂β

∂k. (2.10)

We can also find an explicit expression for the group index in terms of the first-order dispersion in the effective index ne as

ng = ne− λ

∂ne

∂λ. (2.11)

In our case, we only use a small wavelength span around a center wavelength λc.

Therefore we approximate the wavelength-dependence of the eﬀective index ne(λ)

as linear so that β(λ)≈ 2π [ ne(λc)− ng(λc) λc +ng(λc) λ ] . (2.12) 2.1.2 Directional couplers

It is possible to couple light from one waveguide into another by means of a di-rectional coupler. Such a didi-rectional coupler consists of two parallel single-mode waveguides positioned close together as is shown in Figure 2.2a-b. We use a di-rectional coupler to couple a fraction of the light from the straight waveguide into the ring resonator. The electric ﬁeld in the couplerEc _{can be approximated as a}

superposition of the two modes of the isolated waveguides a and b. The amplitudes of the two modes vary along the length of the coupler as is shown in Figure 2.2c. The electromagnetic ﬁeld is approximated as

Ec_{(x, y, z)}_{≈ E}a_{(x, y)u}

a(z) + Eb(x, y)ub(z), (2.13)

with ua and ub the complex modal amplitudes of waveguides a and b respectively

and Ea_{and E}b_{the modal electric ﬁelds of the waveguides. When light propagates}

through waveguide b at the start of the coupler, i.e. z = 0, all energy is in this waveguide and therefore the amplitude of this mode is maximal and the mode in waveguide a is zero (ua(0) = 0). At the eﬀective coupling length of the coupling,

i.e. z = ˜L, the amplitudes of both modes in the coupler is given by

ub( ˜L) = τ ub(0), ua( ˜L) = κub(0). (2.14)

The eﬀective coupling length ˜L = L + ∆L consist of the length of the coupler L and an contribution ∆L from a part of the bends of the waveguide. The complex amplitudes τ and κ are calculated using coupled mode theory. The derivation is

(26)

2.1. Photonic waveguides 11

given in [10], but the ﬁnal formula for the coupling amplitudes for two waveguides is given by τ = ( cos s ˜L−iδ s sin s ˜L ) ei(βb+κbb−δ) ˜L_, _(2.15) κ = − ( iκab s sin s˜l ) ei(βb+κbb−δ) ˜L_, _(2.16)

where βb is the propagation constant of mode b, κbb is the

correc-tion to this propagacorrec-tion constant originating from the other waveguide, δ ≡ 1/2(βb + κbb− βa − κaa) is the diﬀerence between the corrected

propa-gating constants of the guides and s = √κbaκab+ δ2 is the coupling coeﬃcient.

Coupling coeﬃcient κabrepresents the coupling from the mode of waveguide b to

the mode of waveguide a and κbarepresents the coupling from the mode of

waveg-uide a to the mode of wavegwaveg-uide b. These coeﬃcients dominate s. The gwaveg-uides in the coupler that we study are designed to be identical, but we experimentally observed non-zero δ in our couplers.

(a) top-view u_a(0 ) u_b(0 ) u_a( z) u_b( z) ua( ˜L ) ub( ˜L ) x z 0 10 20 0 0.5 1 |u b 2_| |u a 2_| z [µm] pow e r i n m ode (c) (b)

Figure 2.2: Directional coupler and its behavior. a)Top view of a directional

coupler with bus waveguide b and second waveguide a. b) Optical microscope photo of a directional coupler in SOI. The very narrow pinkish lines are the waveguides. c) The normalized power in each mode at a certain coupling length

z. The coupling coeﬃcient s is 0.1 for identical waveguides (δ = 0) [10].

2.1.3 Ring resonators

Ring resonators consist of a looped optical waveguide and a coupling mechanism to couple light into the loop. The shape of the ring is arbitrary. We use racetrack resonators which are elongated rings with a straight part between the bends (Fig. 2.3). As coupling mechanism we use two directional couplers (Sec 2.1.2). A losless coupler without reﬂections is generally described by [16]

( b1 b2 ) = ( τ∗ κ −κ∗ _τ ) ( a1 a2 ) , (2.17)

where a1, a2, b1 and b2 are the waveguide terminals and κ and τ are the coupling

coeﬃcients from the bus waveguide to the ring resonator and vice versa as indicated in Figure 2.3. The relation between the coupling coeﬃcients is given by|τ|2+|κ|2= 1 and the∗ is the complex conjugate.

(27)

When the wave travels through the racetrack resonator it experiences after one round-trip a phase delay ϕρ and a decay by a factor α, so that

a2= αeiϕρb2. (2.18)

We can obtain the power in the output waveguide |b1|2 by substituting Eq.(2.18)

in Eq.(5.1) to ﬁnd b2= −κ∗ 1− ταeiϕρa1, (2.19) and b1= ( τ∗− κκ ∗_αeiϕρ 1− ταeiϕρ ) a1, (2.20)

with τ = |τ|eiϕτ _{and ϕ}

τ the phase delay due to the coupler. We can rewrite

Eq.(2.20) into

b1= −α + |τ|e

i(ϕρ+ϕτ)

e−iϕρ− α|τ|eiϕτ a1. (2.21)

We compute|b1|2= b1b∗1 and use 2 cos θ = eiθ+ e−iθ to get |b1|2=

α2+|τ|2− 2α|τ| cos θ 1 + α2|τ|2− 2α|τ| cos θ|a1|

2_, _(2.22)

where θ = ϕρ+ ϕτis the net phase delay of traveling through the ring and coupler.

In case of two bus waveguides with identical couplers we include the transmis-sion through the second coupler in the track round-trip by replacing α with α|τ|. Eq.(2.23) changes then into

|b1|2=

(α2_{+ 1}_{− 2α cos θ)|τ|}2

1 + α2_|τ|4_{− 2α|τ|}2_{cos θ}|a1|

2_, _(2.23)

with in this case θ = ϕρ+ 2ϕτ. When the racetrack including the couplers has

length l, the transmission through the directional couplers with eﬀective length ˜L is given by Eq. (2.15). The phase delay due to propagation through a waveguide with length l− 2˜L is equal to ϕρ= β(l− 2˜L). The total phase delay of the ring is

therefore given by θ =−βl + 2δ ˜L − 2κbbL + 2arg˜ { cos s ˜L−iδ s sin s˜l } . (2.24)

For a coupler with two identical waveguides, neglecting the κbb and with linear

dispersion of the eﬀective index, the phase delay reduces to θ =−βl = −2π [ ne− ng λc +ng λ ] l, (2.25) with ne≡ ne(λc) and ng≡ ng(λc).

When we measure the transmission spectrum of a waveguide coupled with a single directional coupler to a ring resonator, given by|b1|2as a function of wavelength,

(28)

2.1. Photonic waveguides 13 τ* τ κ -κ* input a1 a2 b2 output b1 (a) τ* τ κ -κ* τ κ a2 b2 drop ad input a₁ output b₁ (b)

Figure 2.3: Sketch of ring resonator and (a) one directional coupler or (b)

two directional couplers. [10].

we observe resonance dips for θ = 2πm with m an integer number. The resonance wavelengths λm for two identical waveguides in the coupler are given by

mλm= ne(λm)l. (2.26)

A typical transmission spectrum for our sensor is shown in Figure 2.4. The diﬀer-ence between two successive resonance dips is indicated by the free spectral range (FSR). We may approximate the FSR by linearizing the relation between m and

λ(m) in Eq.(2.26) and then computing|∆λ| for ∆m = 1 to obtain, ∆λF SR= ∂λ ∂m ∆m = λ2 (ne− λ∂n_∂λe)l = λ 2 ngl . (2.27)

At resonance we have cos θ = 0 and thus Eq.(2.23) becomes |b1|2=

(α− |τ|)2

(1− α|τ|)2|a1|

2_. _(2.28)

This relation shows that there is no transmission at the resonance wavelengths when |τ| = α, hence when the round-trip loss of the racetrack is equal to the power coupled to the racetrack. This condition is called critical coupling. The minimum transmitted power |b1,min|2 occurs at resonance while the maximum

transmitted power |b1,max|2 occurs in between the resonances. The extinction

ratio, deﬁned as r ≡ |b1,min|2/|b1,max|2, and the full-width at half-max (FWHM)

of the transmission spectrum show the shape of the resonances as a function of the waveguide and coupler properties and are given by

r = (α− |τ|) 2_{(1 + α}_|τ|)2 (α +|τ|)2₍₁− α|τ|)2, (2.29) and ∆λF SR= λ2 πlng cos−1 [ 2α|τ| 1 + α2_|τ|2 ] . (2.30)

The FWHM depends on the losses in the resonator and scales with the FSR, while for the extinction ratio the critical coupling is most important. When α is replaced

(29)

by α|τ|, Eq.(2.26)-(2.30) are also valid for two couplers, as the second coupler acts as an additional source of loss.

1530 1540 1550 1560 −40 −30 −20 −10 wavelength [nm] transmittance [dBm/ nm] FSR

Figure 2.4: Measured transmission spectrum of a ring resonator. The FSR

is indicated.

2.2 Membrane deflection

To obtain a sensitive sensor, it is essential to design a membrane with high strain values at the position of the optical ring resonator when it is deformed. In this sub-section, we study the strain distribution on the membrane as well as the resonance frequency of the OMUS.

2.2.1 Static strain proﬁles

For small deflections of the membrane i.e. when the deflections of the plate are small in comparison with the thickness of the plate, the theory of pure bending of plates can be applied. It is assumed that the middle plane, or neutral surface, of the plate does not undergo any extension during bending [17]. When we consider a differential element of a thin plate with a thickness h and area dx dy as is Figure 2.5, the governing equation of the deflection w(r, θ, t) due to an external loading q in polar coordinates is given by [17, 18]

D∇4w(r, θ, t) + ρh∂ 2_{w(r, θ, t)} ∂t2 = q(r, θ, t), (2.31) where∇4=∇2∇2with∇2=_∂r∂22+ 1 r ∂ ∂r+ 1 r2 ∂2

∂θ2 the Laplacian in polar coordinates

and ρ is the density of mass. The ﬂexural rigidity D of the plate is given by

D = E 1− ν2 ∫ h/2 −h/2 z2dz = Eh 3 12(1− ν2₎, (2.32)

(30)

2.2. Membrane deﬂection 15

Figure 2.5: Diﬀerential element of a thin plate with neutral plane n at half

the thickness h of the plate and lamina at z below the middle plane.

with E the Young’s modulus and ν the Poisson ratio. When different materials are used, we integrate over the separate layers with their specific material properties to obtain the flexural rigidity of the entire plate [17].

The displacement w(r, θ, t) measures the deﬂection of the middle plane of the plate. When we look at a lamina with thickness dz located at a distance z below the middle plane n of the plate indicated in Figure 2.5, the normal strains deﬁned as the relative elongation of the lamina (ϵl≡ ∆l/l) are given by

ϵx = z rx , (2.33) ϵy = z ry , (2.34)

where rx and ry are the radii of curvature in the x, z-plane and y, z-plane

respec-tively. We assume small deﬂections and slopes and therefore the curvatures may be approximated with use of the second order derivatives of the displacement (e.g. rx≈ −1/∂ 2_w ∂x2) such that ϵx = −z ∂2_w ∂x2, (2.35) ϵy = −z ∂2_w ∂y2. (2.36)

The shear strain is given by

γxy =−2z

∂2_w

∂x∂y. (2.37)

From Hooke’s law the strains relate to the stresses as

ϵx = 1 E(σx− νσy), (2.38) ϵy = 1 E(σy− νσx), (2.39)

(31)

with ν the Poisson ratio. Combining Eqs. (2.35)-(2.39) results in a radial and transverse stress along the thickness of the membrane in polar coordinates these stresses are σr = Ez 1− ν2 ( ∂2w ∂r2 + ν ∂2w ∂θ2 ) , (2.40) σθ = Ez 1− ν2 ( ∂2_w ∂θ2 + ν ∂2_w ∂r2 ) , (2.41) τrθ = Gγrθ=−2Gz ∂2w ∂r∂θ. (2.42)

In a static situation, Eq. (2.31) can be simpliﬁed to:

D∇4ω(r, θ) = q(r, θ). (2.43)

With a symmetrical load the deﬂection of a circular membrane is independent of θ hence w(r, θ) = w(r). Assuming that the membrane has clamped boundaries, hence w(a) = 0, and ∂w(a)_∂r = 0, and the deﬂection has a maximum at the center of the membrane, i.e.∂w(0)_∂r = 0, this equation can be solved resulting in [17]

w(r) = q

64D (

a2− r2)2. (2.44)

We can determine the maximum or minimum stress at the lower or upper face of the plate. These maximum or minimum stress is the same in the lower and upper face but has an opposite sign. In the radial direction of a face, the absolute maximum is found at the boundary of the plate where σr =−3qa2/(4h2) and a

slightly lower value is found at the center of the plate with opposite sign where σr = 3(1 + ν)qa2/(8h2) [17]. We do not know the exact boundary conditions of

our sensor as the membrane is part of the chip itself. When we therefore model the displacement of the chip under uniform loading we can get the displacement and radial curves for a 100 µm diameter membrane (Fig. 2.6). A typical curve of the radial strain in a layer has positive values at the edge of the membrane where it is extended, while towards the center negative values are present due to a compression of the surface. Between the center and edge is a circular area without radial strain which is around 1/3 of the radius from the edge of the membrane.

2.2.2 Resonance frequency of membranes

To obtain the fundamental mode of the membrane we solve Eq. (2.31) without loading. We assume a solution w(r, θ, t) = W (r, θ)e−iωt with ω the angular fre-quency and t the time. If we go through the mathematics, we ﬁnd the solution for full circular plates as

W (r, θ) ={AJn(βr) + CIn(βr)} [ sin nθ cos nθ ] , (2.45)

with Jnthe Bessel function of the ﬁrst kind, Inthe modiﬁed Bessel function of the

(32)

2.2. Membrane deﬂection 17 −100 −50 0 50 100 −100 −50 0 50 radius [µm] displacement [nm] −0.4 −0.2 0.0 0.2 0.4 microstr a in

Figure 2.6: Typical displacement curve of a circular membrane with a radius

of 50 µm (blue line) and corresponding radial strain curve in a lamina of the plate (red line).

we get

In(βa)Jn′(βa)− Jn(βa)In′(βa) = 0. (2.46)

Each value of n in this equation will have an inﬁnite number of roots, which give the resonance frequencies. We deﬁne λnm = βnma where n is the integer arising

in Eq. (2.46) and m is corresponding to the order of the root for a given n. The fundamental mode has for instance a value of λ2

01 = 10.216. The normal modes

are given by Wnm(r, θ) = { Jn(βnmr)− Jn(βnma) In(βnma) In(βnmr) } [ sin nθ cos nθ ] . (2.47) Because λ2 nm = ωa2 √

ρh/D, we are able to calculate the resonance frequency f = ω/2π in air which is given by [19]

f = 1 2π λ2 nm a2 √ D ρh. (2.48)

One side of the sensor will be submerged in water instead of air, which will give an extra load on the membrane. The resonance frequency will shift downwards by a factor that could be approximated by

fw=

fa

√

1 + γΓ, (2.49)

where fwis the resonance frequency for water, fa the resonance frequency for air,

Γ a non-dimensional added virtual mass factor, which is a function of mode shapes and boundary conditions and γ = ρwa

ρph with ρw the density of mass of the water

(33)

2.3 Membrane modeling

The theory in the previous section demonstrated that the resonance frequency of the membrane can only be exactly determined for air and for known boundary con-ditions. To deal with water loading and unknown boundary conditions we have to solve the problem numerically. We like to obtain values for the ideal thickness of the membrane, given a certain resonance frequency and ﬁnd the corresponding resonance frequency in water of certain membrane diameters. We will ﬁrst de-scribe the modeling parameters followed by the results of the static and dynamic simulations.

2.3.1 Speciﬁcations and modeling parameters

In the numerical simulation we use a 2D axis-symmetric domain and modeled the device as a 250 µm silicon layer below the 2.5 µm SiO2 layer (including the

top layer). The 220 nm thick silicon waveguides are neglected. We assume for simplicity that the strain induced at 0.5 µm from the top, i.e. the waveguide layer, will represent the strain induced in the waveguide. The acoustical membrane is created by removing a part of the substrate. In the static analyses, described in Section 2.3.2, the thickness of silicon left under the SiO2 layer is varied each

time. In the dynamic analyses, described in Section 2.3.2, we model three diﬀerent membranes with diameters of 60 µm, 80 µm and 100 µm. In these dynamic models, the membranes consist only of SiO2, and the area underneath the membrane is

filled with air. The remaining part of the modeling domain is filled with water. The discretization of the receiver design contained at least 12 points per wavelength. The water domain is large enough to avoid interference from reflecting waves from the boundaries of the domain. In both studies we used a density of mass of 2329 kg/m3 _{for the silicon and an isotropic Young’s modulus of 170 GPa and}

Poisson ratio of 0.28. The silica has a density of 2200 kg/m3_{, Young’s modulus of}

70 GPa and a Poisson ratio of 0.17.

2.3.2 Modeling results

To analyze the strain profiles and determine the response of the receiver, we per-form two different analyses which are described in this section. The first part is a static analysis by which we compute the dimensions of the membrane. The second part is a dynamic study in which the response and sensitivity of the receiver are obtained.

Static analysis

The acoustical membrane can be developed for all kinds of applications. We de-signed a membrane that has an acoustical resonance at 1 MHz when it is submerged in water. To ﬁnd the optimal dimensions, i.e. inducing the highest amount of strain in the optical resonator, we investigate whether an optimum is present when the thickness of the membrane is varied. The thickness of the membrane consists of at least the 2.5 µm SiO2layer, so only the thickness of the silicon was varied from

(34)

2.3. Membrane modeling 19

Table 2.1: Response of three prototype receivers due to an incident plane

wave

Membrane Resonance Sensitivity Minimum detection

diameter [µm] frequency [MHz] [microstrain/kPa] level [Pa]

60 3.2 1.3 1540

80 1.6 3.4 590

100 0.9 3.2 625

0 µm to 10 µm. For each thickness of the membrane the corresponding radius is calculated by Eqs. (2.48) and (2.49) to obtain a resonance frequency of 1 MHz. For every thickness and corresponding radius, we determine with a ﬁnite element model the maximum absolute strain that can be induced in the membrane. We used a static pressure of 1 kPa. The results show that the maximum strain varies from 0.17 to 0.45 microstrain. The maximum value is attained when 1.2 µm of silicon is left underneath the 2.5 µm SiO2 layer.

Although an optimum exists, the difference in strain in the range of 0 µm to 4 µm of silicon is only a factor of 1.5. In the fabrication process of the membrane, the flatness and thickness of the silicon layer is difficult to control. A well-controlled fabrication can be performed when all the silicon up to the SiO2layer is removed,

using a chemically selective etch process. Therefore we have ﬁnally choosen to remove all the silicon in the design of the prototypes and in the remaining study.

Dynamic analysis

We designed three prototypes with different membrane diameters to determine the response and influence of the membrane on the performance of the sensor. In a time domain analysis, we used an incident acoustic plane wave with Gaussian pulse shape with a maximum amplitude of 50 kPa and pulse width of 0.6 µs. The time and frequency response of the 80 µm diameter membrane are shown in Figure 2.7. The results of all the receivers are listed in Table 2.1. For every receiver, we numerically obtained the resonance frequency of the membrane. The maximum strain values, present in the time simulations, were used to calculate the sensitivity by dividing the strain by the maximum of the incoming pressure field. To determine the minimum pressure detection level, we assumed to have an optical detector with a resolution of 1 pm and we used 0.5 pm/microstrain for the shift in the light spectrum due to strain from [21].

The results show that our device can be well used for ultrasound sensing. The three times less sensitivity of the smallest membrane suggest that there is a minimum footprint of the element. Furthermore, we conclude that the membrane with a 80 µm diameter is the most sensitive receiver.

(35)

20 Chapter 2. Basic concepts and membrane design 0 2 4 6 8 −150 −100 −50 0 50 100 150 time [µs] Microstrain

Induced strain (d = 80 µm) in water

0 5 10 15 20 −100 −80 −60 −40 −20 0 frequency [MHz] Amplitude [dB]

Frequency response in water

1.6 MHz

a) b)

Figure 2.7: a) The induced strain by a propagating Gaussian pressure wave

and b) the frequency response of the 80 µm diameter membrane. Both plots apply to the center point of the waveguide layer.

2.4 Conclusion

With use of the basic concepts of waveguides and membrane deflection we have been able to design a prototype sensor. When we look at the static strain profiles we conclude that the optical resonator needs to be positioned at maximum dis-tance from the neutral plane, i.e. at the top or at the bottum, and either in the center or at the edge of the membrane. When the sensor is realized, the waveg-uide needs to be protected from the water and will therefore be positioned below a 0.5 µm cladding. Therefore the maximum distance from the neutral plane is a little bit less in the final design. Because of the current racetrack shape of the ring resonators we will position it in the center of the membrane where the largest area with similar strain values is present. Because this area with similar strain is lim-ited, the maximum length of the ring resonator is limited to 2/3 of the membrane diameter.

The thickness of the membrane should in optimal situation contain a layer of 1.2 µm silicon underneath the silicondioxide for a membrane with resonance around 1 MHz. Although this optimum exist we prefer to build a prototype that could easily be compared to models and hence contains a ﬂat and evenly thick membrane. Therefore we will remove all the silicon with a well-controlled chemically selective etch process.

The dynamic simulations show that the obtained sensitivity of the sensor is suﬃ-cient for ultrasound sensing. Furthermore is it possible to fabricate the membrane diameters that correspond to resonance frequencies in the MHz range.

(36)

Chapter

3

Optical characterization of

strain sensors based on

silicon waveguides

Abstract – Microscale strain gauges are widely used in micro electro-mechanical

systems (MEMS) to measure strains such as those induced by force, acceleration, pressure or sound. We propose all-optical strain sensors based on micro-ring res-onators to be integrated with MEMS. We characterized the strain-induced shift of the resonances of such devices. Depending on the width of the waveguide and the orientation of the silicon crystal, the linear wavelength shift per applied unit of strain varies between 0.5 and 0.75 pm/microstrain for infrared light around 1550 nm wavelength. The influence of changing ring circumference is about three times larger than the influence of the change in waveguide effective index, and the two effects oppose each other. The strong dispersion in 220 nm high silicon sub-wavelength waveguides accounts for a decrease in sensitivity of a factor 2.2 to 1.4 for waveguide widths of 310 nm to 860 nm. These figures and insights are necessary for the design of strain sensors based on silicon waveguides.

This chapter is based on the following publication:

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi and H. P. Urbach “Characterization of integrated optical strain sensors based on silicon waveguides,” in JSTQE, Vol. 11, No. 4, December 2013

Earlier results based on micro-ring resonators where we excited the fundamental TM-like mode of a 300 nm high silicon waveguide were published as W.J. Westerveld, J. Pozo, P.J. Harmsma, R. Schmits, E. Tabak, T.C. van den Dool, S.M. Leinders, K.W.A. van Dongen, H.P. Urbach, and M. Yousefi, “Characterization of a photonic strain sensor in silicon-on-insulator technology,” Optics Letters, vol. 37, no. 4, pp. 479–481, Feb 2012.

(37)

22 Chapter 3. Optical characterization of strain sensors based on waveguides

3.1 Introduction

Microscale strain gauges are widely used in micro electro-mechanical systems (MEMS) to measure strains such as those induced by force, acceleration, pressure or (ultra)sound [22, 23]. These sensors are traditionally based on a piezoresistive or piezoelectric material which transduces the strain to an electrical signal. Alter-natively, optical resonators can be used as sensing element, providing particular beneﬁts: high-speed readout, small sensor size, small multiplexer size (1 mm2_),

in-sensitivity to electromagnetic interference, and no danger of igniting gas explosions with electric sparks.

Integrated optics technology allows the optical strain sensors, as well as their tiplexing circuit, to be integrated with MEMS. The sensing elements and their mul-tiplexers can often be fabricated in a single processing step. Silicon-on-insulator (SOI) has emerged as one of the focus platforms for integrated optics, and is rel-atively straightforward to integrate with MEMS, as MEMS are most commonly made of silicon. Micro-electronic research institutes have tailored CMOS fabrica-tion processes to the demands of SOI optical circuits, and now oﬀer cheap and reproducible wafer-scale fabrication [24, 25]. The high contrast of the refractive index of SOI ridge waveguides allows for a small device footprint, and single-mode guides have a cross-section of only 400× 220 nm2_.

We employ ring resonators as sensing element. Such a resonator consists of a wave-guide which is looped, forming a closed cavity which has speciﬁc optical resonance wavelengths. Any change in the size or in the refractive index of this waveguide shifts its resonances, and this shift can be accurately recorded.

Several groups have reported on sensor micro opto-electro-mechanical systems (MOEMS) that are based on silicon integrated optical ring resonators, such as strain gauges [26, 27], or pressure sensors [28–30]. An application of particular interest is as ultrasound sensor for medical intravascular ultrasonography (IVUS). IVUS has been recommended for the diagnostics of atherosclerosis [31, 32]. IVUS is an invasive technique for blood vessel imaging where the sensor is attached to a catheter and brought inside the artery. Using an array of sensors improves the image quality but wiring many piezoelectric sensors with coaxial cables requires too much space for this application. As solution, we proposed a micro-machined ultrasound transducer (MUT) with optical readout [33]. This sensor consists of a silicon ring resonator integrated in a membrane that deforms due to ultrasonic waves. Integrated optical multiplexers allow high-speed read-out of many sensors via one optical ﬁber and, moreover, insensitivity to electromagnetic interference allows usage inside MRI scanners.

The relation between strain and silicon waveguides is of broader interest than sens-ing. Electro-mechanical modulation of silicon optical resonators may be employed to modulate optical signals, for application in the field of telecommunication [34]. As alternative to silicon waveguide-based ring resonators, it is also possible to use photonic crystals cavities, which have their own dispersion relations [35]. Strain has also been used to modify the birefringence of larger SOI rib waveguides [36]. Strain is inevitable when using silicon photonic circuits on a flexible substrate [37]. Another interesting field of research is the strain-induced change in the electronic

Characterization of a novel Optical Micro-machined Ultrasound Transducer

Delft University of Technology

Characterization of a novel Optical Micro-machined Ultrasound Transducer

Characterization of a novel

Optical Micro-machined Ultrasound Transducer

Summary

Samenvatting

Contents

1

General introduction

1.1

Medical imaging

1.2

An optical micro-machined ultrasound sensor

for (medical) ultrasound

1.3

Integrated

photonic

systems

and

micro-machining fabrication technology

1.4

Outline of this thesis

2

Basic concepts and

membrane design

2.1

Photonic waveguides

2.2

Membrane deflection

2.3

Membrane modeling

2.4

Conclusion

3

Optical characterization of

strain sensors based on

silicon waveguides

3.1

Introduction